Andrew Steane discusses multiple particle interference and quantum error correction, drawing parallels with classical error correcting codes. He shows that quantum error correction can be understood through the lens of classical information theory, allowing for the protection of quantum information against decoherence. The key idea is that quantum information can be encoded in multiple qubits, enabling error correction that reduces the impact of decoherence. The paper demonstrates that a quantum channel can recover from arbitrary decoherence of x qubits if K bits of quantum information are encoded using n quantum bits, where K/n can be greater than 1 - 2H(2x/n), but must be less than 1 - 2H(x/n). This implies exponential reduction of decoherence with only a polynomial increase in computing resources. The methods also allow isolation of quantum communication from noise and eavesdropping. The paper introduces the concept of multiple particle interference, showing that it can be understood through parity checks. It then discusses error correction for qubits, showing that single-qubit errors can be corrected using a repetition code. The paper also discusses the generalization of these methods to correct multiple qubit errors, and shows that the encoding and correction procedures can be used to amplify quantum privacy. The paper concludes that quantum computation can be made error-free in the presence of realistic levels of decoherence, and that the methods allow for the protection of quantum information against errors.Andrew Steane discusses multiple particle interference and quantum error correction, drawing parallels with classical error correcting codes. He shows that quantum error correction can be understood through the lens of classical information theory, allowing for the protection of quantum information against decoherence. The key idea is that quantum information can be encoded in multiple qubits, enabling error correction that reduces the impact of decoherence. The paper demonstrates that a quantum channel can recover from arbitrary decoherence of x qubits if K bits of quantum information are encoded using n quantum bits, where K/n can be greater than 1 - 2H(2x/n), but must be less than 1 - 2H(x/n). This implies exponential reduction of decoherence with only a polynomial increase in computing resources. The methods also allow isolation of quantum communication from noise and eavesdropping. The paper introduces the concept of multiple particle interference, showing that it can be understood through parity checks. It then discusses error correction for qubits, showing that single-qubit errors can be corrected using a repetition code. The paper also discusses the generalization of these methods to correct multiple qubit errors, and shows that the encoding and correction procedures can be used to amplify quantum privacy. The paper concludes that quantum computation can be made error-free in the presence of realistic levels of decoherence, and that the methods allow for the protection of quantum information against errors.